The potential energy surfaces (PESs) and free energy surfaces (FESs) of all 10 canonical and methylated nucleic acid base pairs were studied by a molecular dynamics/quenching (MD/Q) technique with the Cornell et al. empirical force field and by a correlated ab initio quantum chemical method. More than a dozen energy minima were located on the PES of each base pair. The global and first local minima of nonmethylated base pairs have a systematically planar H-bonded structure, while T-shaped and stacked structures are less stable. The MD/Q search sometimes reveals an unexpected structure as the global energy minimum (e.g., the global minimum of the adenine...thymine PES corresponds neither to the Watson-Crick nor the Hoogsteen type of bonding). Entropy does not play an important role and the relative order of individual structures on the PES and FES does not differ too much. Methylation at purine N9 and pyrimidine N1 brings dramatic changes in the PESs and FESs, mainly because the most stable and most populated H-bonded structures are eliminated. In the case of methylated base pairs entropy plays an important role and the structure of the global minimum does not usually correspond to the most populated structure: frequently, it is the stacked structure which is the most populated. Theoretical calculations reveal that the PESs and FESs of most base pairs are very complex and are characterized by the coexistence of several structures, which makes assignment of various experimental characteristics difficult or even unfeasible. In the case of PESs, the only exceptions were guanine...cytosine and guanine...guanine pairs and their methylated analogues. The respective PESs contained one or two stable structures while the other structures were significantly less stable. Further, three pairs (cytosine...thymine, guanine...guanine, and guanine...thymine) possessed simple FESs at 300 K, where one or two structures were populated considerably motre than the others.